In recent years, there is an attempt to control the traveling of each vehicle, thereby improving the amount of traffic on the road and reducing traffic congestion. For example, Patent Literature 1 discloses a vehicle-in-front following device which detects a change in the gradient of the front side of the road and changes the control mode from inter-vehicle distance control to vehicle speed control when a change in the gradient is detected in front of the road in the vicinity of, for example, a sag section (position where the road is changed from a descent to an ascent). In the vehicle-in-front following device disclosed in Patent Literature 1, the control mode is changed from inter-vehicle distance control to vehicle speed control in the vicinity of the sag section, thereby suppressing a change in the vehicle speed during vehicle-in-front following control. In particular, the vehicle-in-front following device disclosed in Patent Literature 1 prevents a phenomenon in which a change in the speed of the vehicle in front is amplified and propagated to the following vehicle even though the gradient is changed in the sag section when a plurality of vehicles travel in a line.